Spreadsheet Project: Using Excel to Explore Slope and Y-Intercept of Functions

Introduction: Standards, Goals and Objectives of the Project

My experiences using Excel in the classroom as a teaching tool is non-existent. I have used it for my own purposes – mainly keeping track of student data. As a paraprofessional, I used it to record student’s benchmark scores, their end of quarter grades, CMT scores, and any special needs the student had. This allowed me to have an overall picture of the students – where they had come from and how they were progressing. While student teaching I have also used Excel in a similar manner, keeping track of student’s pre-and –post-test scores in specific units to plan teaching, see growth, and look for area needed for reteaching. I have also used spreadsheets in my own learning – not for math – but for my senior history seminar. I used a spreadsheet to transfer Census Data from unreadable PDFs to Excel in order to be able to get a ballpark estimate on the number of Italians in Willimantic as well as be able to analyze their occupations, number of children, and other census data more easily. I found it extremely beneficial because it saved me hours of having to scroll through fuzzy screenshots. Although it was initially a lot of work to transfer the data from PDF to Excel, it made analyzing the data a lot easier.

There is a lot of unexplored potential in using Spreadsheets at both the secondary and elementary level. Other Microsoft software such as Word and PowerPoint, and even Publisher, get used often in the classroom but Spreadsheets tend to be overlooked. The NCTM Standards do not specifically mention the use of spreadsheets but the process standards, specifically the Representation standard, do: “Create and use representations to organize, record, and communicate mathematical ideas” (NCTM, 2000). In the Common Core State Standards for Math under Standards for Mathematical Practice, it emphasizes using appropriate tools strategically. These tools include spreadsheets and the goal is for students who are “making mathematical models…know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data” (CCSS, 2010, p. 7). In high school algebra, students are expected to use “a spreadsheet or a computer algebra system (CAS) can be used to experiment with algebraic expressions, perform complicated algebraic manipulations, and understand how algebraic manipulations behave” (CCSS, 2010, p. 62). Additionally, it also states “sometimes functions are defined by a recursive process, which can be displayed effectively using a spreadsheet or other technology” (CCSS, 2010, p. 67).

As described by Chrisler (2013), spreadsheets can be used to “grab students attention” and “encourage students to think about math in novel ways as well as enhance student learning on the concepts and skills that spreadsheets can model” (p. 418-419). Chrisler also mentions the importance of knowing how to teach with spreadsheets. It is important that the teacher has an understanding of the capabilities of the spreadsheet and is able to explain certain tasks before they attempt to teach using this tool. A lack of knowledge will lead to frustration on the part of both teacher and students.

Neurath and Stephens (2006) explain “teachers are continuously looking for methods to increase interest in algebra, which will, in turn, increase achievement in the course” (p. 721). The authors use Excel in hopes that it will lead to an increase in student interest and ability. The results of Neurath and Stephens study was an increase in student attitude towards algebra after participating in the Excel experimental group, as well as an increase in student achievement on the final exam.

This project will demonstrate how Excel can be used to graph functions at the middle school level. More specifically, the project has the following objectives:

This project meets the 8th grade CCSS standard 8.F.5:”Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally” CCSS, 2010, p.55). The project meets different student’s needs by having two worksheets. Worksheet 1 is geared towards students who are ready for this standard but might need more scaffolding while Worksheet 2 is aimed towards students who are ready to explore more in-depth the relationship between slope and y-intercept on the resulting coordinates without teacher assistance. Worksheet 1 is to be completed by all students while Worksheet 2 is for students who are ready for work with less scaffolding.

The activities are intended to be completed in an 8th grade pre-algebra class in a whole class setting and should be completed in two 45-minute periods. The project will lead to a higher conceptual level of understanding by the students of functions, graphing the functions and how changing slope and the y-intercept affect the graph. As described by Chrisler (2013), Excel will be used to “extend their thinking about functions, apply the relationship between input and output, work with larger numbers, or reveal the visual representation of more complex functions” (p. 422). Additionally as explained by Thatch and Norman(2008), “students use computer technology to present ideas and represent concepts, manipulate variables and objects in ways that are difficult to accomplish with paper and pencil, and explore problems in greater depth” (p. 152). This Excel project will allow students to accomplish all of these goals.

Project Activities

Step 1

. Students will already have been working with functions, creating coordinates charts, graphing functions, and have been introduce to the concepts of slope and y-intercept. Students will begin by completing a coordinate chart with the x coordinates of 0, 1, 2 and students will identify the y-intercept, and the slope for the function f(x) = 4x -3. They will do this for homework without the use of technology.

Step 2

. Students will then follow the instructions on their worksheet to set up the coordinates chart on Excel. Students will extend the chart to include x coordinates of 0, 1, 2, 3, 4, 5.

Step 3

. Students will then copy and paste to create a second coordinate table next to the first one. Students will then create graphs for both functions following the instructions on their worksheet.

Step 4

. Students will alter the slope and y-coordinate following the worksheet instructions and answer the worksheet questions. Doing this will allow them to compare the first function to the second to see the effect changing positive to negative and changing different numbers has on the graph itself.

Step 5

. Students who are ready to explore more in-depth the relationship between slope, y-intercept and coordinate points will complete Worksheet 2. Worksheet 2 has students further exploring how changing the slope and y-intercept at the same time affects the graph. Students will ultimately create their own functions and graph them.

Final Thoughts

I have never taught using this activity before but I have worked with students in an intervention setting providing support in solving functions. While these students are able to graph the functions, they have low levels of understanding in what they are graphing and the effect different signs and different numbers has on the graph itself. I hope this activity would lead to a better understanding of these concepts. It is my plan to implement this activity with the students to supplement their classroom instruction. I do worry that Worksheet 1 on its own might not be thorough enough for students to gain a complete understanding of functions and the relationships between slope and the y-intercept.